Lithium-ion batteries SOH estimation based on gaussian processed regression optimized by egret swarm optimization

doi:10.19799/j.cnki.2095-4239.2025.0021

Abstract

Abstract:

Accurate estimation of the state of health (SOH) of lithium-ion batteries is essential for ensuring the safety and reliability of battery systems and is a critical function of battery management systems. To address the limitations of existing data-driven SOH estimation methods—such as inadequate representation of uncertainty and insufficient decoupling of training and testing data—this study proposes a novel approach based on Gaussian process regression (GPR) optimized by the egret swarm optimization algorithm (ESOA). Health features related to battery aging are extracted from the charging voltage, current, and relaxation voltage data of similar batteries, and features with high correlation to capacity are selected using Pearson correlation analysis. A GPR model employing a squared exponential kernel is then used for SOH estimation, with its hyperparameters optimized via ESOA. The proposed method is validated using NCA and NCM battery datasets from Tongji University. Experimental results show that the method significantly improves estimation accuracy and robustness. For the tested batteries, the maximum root mean square error (RMSE) and mean absolute error (MAE) are 0.0028 and 0.22%, respectively, representing improvements of 58.82% and 57.69% over conventional GPR models. Additionally, the method enables SOH interval estimation, reducing the risk of safety hazards from overestimation.

Key words: lithium-ion battery, state of health, egret swarm optimization algorithm, Gaussian process regression, interval estimation

CLC Number:

TM 912

Chunling WU, Liding WANG, Yong LU, Limin GENG, Hao CHEN, Jinhao MENG. Lithium-ion batteries SOH estimation based on gaussian processed regression optimized by egret swarm optimization[J]. Energy Storage Science and Technology, 2025, 14(6): 2498-2511.

Figures/Tables 13

Table 1

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Table 2

Fig. 5

Fig. 6

Fig. 7

Table 3

Fig. 8

Fig. 9

Table 4

References 26

1	杨夯, 黄小庆, 于慎仟, 等. 电化学储能电站主动安全研究[J]. 电力自动化设备, 2023, 43(8): 78-87. DOI: 10.16081/j.epae.202209017.YANG H, HUANG X Q, YU S Q, et al. Research on active safety of electrochemical energy storage station[J]. Electric Power Automation Equipment, 2023, 43(8): 78-87. DOI: 10.16081/j.epae. 202209017.
2	ZHENG Y X, HU J X, CHEN J J, et al. State of health estimation for lithium battery random charging process based on CNN-GRU method[J]. Energy Reports, 2023, 9: 1-10. DOI: 10.1016/j.egyr. 2022.12.093.
3	DINI P, COLICELLI A, SAPONARA S. Review on modeling and SOC/SOH estimation of batteries for automotive applications[J]. Batteries, 2024, 10(1): 34. DOI: 10.3390/batteries10010034.
4	LI X Z, ZHANG L Z, LIU Y, et al. A fast classification method of retired electric vehicle battery modules and their energy storage application in photovoltaic generation[J]. International Journal of Energy Research, 2020, 44(3): 2337-2344. DOI: 10.1002/er.5083.
5	赵鹤, 韩策, 程小露, 等. 采用阳极预锂化技术的锂离子电池高倍率老化容量衰减机理研究[J]. 储能科学与技术, 2021, 10(2): 454-461. DOI: 10.19799/j.cnki.2095-4239.2020.0340.
	ZHAO H, HAN C, CHENG X L, et al. Research on the capacity fading mechanism of high rate aged lithium-ion batteries with anode prelithiation treatment[J]. Energy Storage Science and Technology, 2021, 10(2): 454-461. DOI: 10.19799/j.cnki.2095-4239. 2020.0340.
6	BASIA A, SIMEU-ABAZI Z, GASCARD E, et al. Review on state of health estimation methodologies for lithium-ion batteries in the context of circular economy[J]. CIRP Journal of Manufacturing Science and Technology, 2021, 32: 517-528. DOI: 10.1016/j.cirpj. 2021.02.004.
7	CHANG C, WANG Q Y, JIANG J C, et al. Lithium-ion battery state of health estimation using the incremental capacity and wavelet neural networks with genetic algorithm[J]. Journal of Energy Storage, 2021, 38: 102570. DOI: 10.1016/j.est. 2021. 102570.
8	STROE D I, SCHALTZ E. Lithium-ion battery state-of-health estimation using the incremental capacity analysis technique[J]. IEEE Transactions on Industry Applications, 2020, 56(1): 678-685. DOI: 10.1109/TIA.2019.2955396.
9	CHEN Y P, HUANG M H. A method of battery state of health prediction based on AR-particle filter[C]//SAE Technical Paper Series. SAE International, 2016: DOI: 10.4271/2016-01-1212.
10	FU J C, WU C L, WANG J W, et al. Lithium-ion battery SOH prediction based on VMD-PE and improved DBO optimized temporal convolutional network model[J]. Journal of Energy Storage, 2024, 87: 111392. DOI: 10.1016/j.est.2024.111392.
11	FENG X N, WENG C H, HE X M, et al. Online state-of-health estimation for Li-ion battery using partial charging segment based on support vector machine[J]. IEEE Transactions on Vehicular Technology, 2019, 68(9): 8583-8592. DOI: 10.1109/TVT. 2019. 2927120.
12	巫春玲, 吕晶晶, 相里康, 等. 基于变分模态分解和核极限学习机集成模型的电动汽车锂电池健康状态预测[J/OL]. 电源学报, 2023: 1-14. (2023-09-20). https://kns.cnki.net/KCMS/detail/detail.aspx?filename=DYXB20230918002&dbname=CJFD&dbcode=CJFQ.
	WU C L, LÜ J J, XIANGLI K, et al. Health state prediction of electric vehicle lithium battery based on integrated model of variation modal decomposition and kernel limit learning machine[J/OL]. Journal of Power Supply, 2023: 1-14. (2023-09-20). https://kns.cnki.net/KCMS/detail/detail.aspx?filename=DYXB20230918002&dbname=CJFD&dbcode=CJFQ.
13	WU C L, FU J C, HUANG X R, et al. Lithium-ion battery health state prediction based on VMD and DBO-SVR[J]. Energies, 2023, 16(10): 3993. DOI: 10.3390/en16103993.
14	RAUF H, KHALID M, ARSHAD N. Machine learning in state of health and remaining useful life estimation: Theoretical and technological development in battery degradation modelling[J]. Renewable and Sustainable Energy Reviews, 2022, 156: 111903. DOI: 10.1016/j.rser.2021.111903.
15	顾菊平, 蒋凌, 张新松, 等. 基于特征提取的锂离子电池健康状态评估及影响因素分析[J]. 电工技术学报, 2023, 38(19): 5330-5342. DOI: 10.19595/j.cnki.1000-6753.tces.231085.
	GU J P, JIANG L, ZHANG X S, et al. Estimation and influencing factor analysis of lithium-ion batteries state of health based on features extraction[J]. Transactions of China Electrotechnical Society, 2023, 38(19): 5330-5342. DOI: 10.19595/j.cnki.1000-6753.tces.231085.
16	ZHU J G, WANG Y X, HUANG Y, et al. Data-driven capacity estimation of commercial lithium-ion batteries from voltage relaxation[J]. Nature Communications, 2022, 13: 2261. DOI: 10. 1038/s41467-022-29837-w.
17	李放, 闵永军, 王琛, 等. 基于充电过程的锂电池SOH估计和RUL预测[J]. 储能科学与技术, 2022, 11(10): 3316-3327. DOI: 10.19799/j.cnki.2095-4239.2022.0165.
	LI F, MIN Y J, WANG C, et al. State of health estimation and remaining useful life predication of lithium batteries using charging process[J]. Energy Storage Science and Technology, 2022, 11(10): 3316-3327. DOI: 10.19799/j.cnki.2095-4239. 2022. 0165.
18	张朝龙, 陈阳, 刘梦玲, 等. 一种基于ICA-T特征和CNN-LA-BiLSTM的锂离子电池健康状态估计方法[J]. 储能科学与技术, 2025, 14(3): 1258-1269. DOI:10.19799/j.cnki.2095-4239.2024.1124.
	ZHANG C L, CHEN Y, LIU M L, et al. A state of health estimation method for lithium-ion batteries using ICA-T features and CNN-LA-BiLSTM[J]. Energy Storage Science and Technology, 2025, 14(3): 1258-1269. DOI:10.19799/j.cnki.2095-4239.2024.1124.
19	WEN J P, CHEN X, LI X H, et al. SOH prediction of lithium battery based on IC curve feature and BP neural network[J]. Energy, 2022, 261: 125234. DOI: 10.1016/j.energy.2022.125234.
20	ZHAO Y P, WANG J J, LI X Y, et al. Extended least squares support vector machine with applications to fault diagnosis of aircraft engine[J]. ISA Transactions, 2020, 97: 189-201. DOI: 10. 1016/j.isatra.2019.08.036.
21	REEVES B. Noise modulated GPR: Second generation technology[C]//Proceedings of the 15th International Conference on Ground Penetrating Radar. June 30-July 4, 2014, Brussels, Belgium. IEEE, 2014: 708-713. DOI: 10.1109/ICGPR. 2014. 6970519.
22	李晓燕, 李弢, 马尽文. 高斯过程混合模型在含噪输入预测策略下的煤矿瓦斯浓度柔性预测[J]. 信号处理, 2021, 37(11): 2031-2040. DOI: 10.16798/j.issn.1003-0530.2021.11.003.
	LI X Y, LI T, MA J W. Soft prediction of coal-mine gas concentration through the mixture of Gaussian processes under the noisy input prediction strategy[J]. Journal of Signal Processing, 2021, 37(11): 2031-2040. DOI: 10.16798/j.issn.1003-0530.2021.11.003.
23	徐厚宝, 杨承莲, 张永康. 卡尔曼滤波优化的高斯过程回归模型[J]. 北京理工大学学报, 2024, 44(5): 538-545. DOI: 10.15918/j.tbit1001-0645.2023.211.
	XU H B, YANG C L, ZHANG Y K. Optimization model of Gaussian process regression based on Kalman filtering[J]. Transactions of Beijing Institute of Technology, 2024, 44(5): 538-545. DOI: 10.15918/j.tbit1001-0645.2023.211.
24	SHAMI T M, EL-SALEH A A, ALSWAITTI M, et al. Particle swarm optimization: A comprehensive survey[J]. IEEE Access, 2022, 10: 10031-10061.
25	LI C R, XIAO F, FAN Y X, et al. An approach to lithium-ion battery SOH estimation based on convolutional neural network[J]. Transactions of China Electrotechnical Society, 2020, 35(19): 4106-4119. DOI: 10.19595/j.cnki.1000-6753.tces.191617.
26	CHEN Z Y, FRANCIS A, LI S, et al. Egret swarm optimization algorithm: An evolutionary computation approach for model free optimization[J]. Biomimetics, 2022, 7(4): 144. DOI: 10.3390/biomimetics7040144.

电池类型	NCA电池	NCM电池
电池类型	18650	18650
阳极材料	Graphite/Si	Graphite
阴极材料	Li_0.86(Ni_0.86Co_0.11Al_0.03)O₂ (NCA)	Li_0.84(Ni_0.83Co_0.11Mn_0.07)O₂ (NCM)
电解液	—	非水溶剂与LiPF₆
额定电压	—	3.60 V
截止电压	2.65~4.20 V	2.50~4.20 V
额定容量	3.5 Ah	3.5 Ah
电池质量	—	45.0 g

电池编号	特征参数
电池编号	HF1 (DCEVI)	HF2 (DCECI)	HF3 (voltage max)	HF4 (voltage drop)
NCA1	0.9982	0.9985	0.9680	0.9834
NCA2	0.9987	0.9996	0.9803	0.9904
NCA3	0.9968	0.9973	0.9862	0.9880
NCA4	0.9959	0.9990	0.9804	0.9909
NCM1	0.9956	0.9998	0.9932	0.9942
NCM2	0.9962	0.9982	0.9978	0.9978
NCM3	0.9928	0.9980	0.9934	0.9936
NCM4	0.9951	0.9991	0.9942	0.9941

电池编号	计算耗时/s
电池编号	GRU	LSTM	BP	PSO-BP	ESOA-BP	GPR	PSO-GPR	ESOA-GPR
NCA1	0.00999	0.01157	0.17290	0.00984	0.00994	0.01642	0.01437	0.01621
NCA2	0.01382	0.01072	0.10458	0.00705	0.00818	0.01977	0.01682	0.01388
NCA3	0.01272	0.01246	0.01999	0.00950	0.00726	0.00625	0.00639	0.00651
NCA4	0.01597	0.01735	0.01006	0.00804	0.009289	0.01873	0.02061	0.01897

电池编号	计算耗时/s
电池编号	GRU	LSTM	BP	PSO-BP	ESOA-BP	GPR	PSO-GPR	ESOA-GPR
NCM1	0.01371	0.01103	0.00963	0.00920	0.00890	0.00620	0.00810	0.00636
NCM2	0.01471	0.01500	0.00813	0.00684	0.00694	0.01364	0.01161	0.02107
NCM3	0.01046	0.01362	0.00867	0.00761	0.00737	0.01305	0.01221	0.01565
NCM4	0.01847	0.01233	0.00737	000732	0.00690	0.02433	0.02319	0.02668

[1]	Jiahui LIU, Weixiang BIAN, Dawei LI. In situ measurement and analysis of the electromechanical coupling performance of composite graphite electrodes in lithium batteries [J]. Energy Storage Science and Technology, 2025, 14(6): 2240-2247.
[2]	Huimin FAN, Haohong PENG, Hui MENG, Menghong TANG, Haohao YI, Jing DING, Jincheng LIU, Chengshan XU, Xuning FENG. Research and simulation analysis of swelling force characteristics in energy storage battery modules [J]. Energy Storage Science and Technology, 2025, 14(6): 2488-2497.
[3]	Zheng CHEN, Gongdong DUO, Jiangwei SHEN, Shiquan SHEN, Yu LIU, Fuxing WEI. State of health estimation for lithium battery based on incremental capacity analysis and VMD-GWO-KELM [J]. Energy Storage Science and Technology, 2025, 14(6): 2476-2487.
[4]	Gongrui WANG, Anping ZHANG, Xuanxuan REN, Mingzhe YANG, Yuning HAN, Zhongshuai WU. High-voltage lithium cobalt oxide cathode: Key challenges, modification strategies and future prospectives [J]. Energy Storage Science and Technology, 2025, 14(6): 2278-2319.
[5]	Haiyang ZHOU, Zhendong ZHANG, Lei SHENG, Zehua ZHU, Xiaojun ZHANG, Chunfeng ZHANG. Simulation of immersion thermal performance regulation and thermal safety experimental study for energy storage lithium batteries [J]. Energy Storage Science and Technology, 2025, 14(5): 1866-1874.
[6]	Zhoulan ZENG, Lei SHANG, Zhijin HU, Zongfan WANG, Xiaochao XIN, Ying LIU. Li₅FeO₄@C high capacity prelithium cathode materials for lithium-ion batteries [J]. Energy Storage Science and Technology, 2025, 14(5): 1875-1883.
[7]	Ping DING, Taotao LI, Linfeng ZHENG, Weixiong WU. SOH estimation of real-world power batteries based on Soft-DTW algorithm and multisource reature fusion [J]. Energy Storage Science and Technology, 2025, 14(5): 2081-2097.
[8]	Ziming MO, Zongxin RAO, Jianfei YANG, Menghao YANG, Liming CAI. Construction and characteristic analysis of key parameters in a gas-thermal model for thermal runaway in lithium-ion battery based on overcharge [J]. Energy Storage Science and Technology, 2025, 14(5): 1784-1796.
[9]	Lei PENG, Zhaopeng NI, Yue YU, Fupeng SUN, Xiulong XIA, Peng ZHANG, Sibo SUN. Experimental study on NCM lithium-ion battery electric vehicle fire caused by overcharging [J]. Energy Storage Science and Technology, 2025, 14(4): 1484-1495.
[10]	Jiangwei SHEN, Yixin SHE, Xing SHU, Yonggang LIU, Fuxing WEI, Xuelei XIA, Zheng CHEN. State of health estimation for lithium batteries based on short-term random charging data and optimized convolutional neural network [J]. Energy Storage Science and Technology, 2025, 14(4): 1585-1595.
[11]	Ruihao LIU, Xiaole MA, Yuxuan ZHANG, Yueying ZHU, Shiqiang LIU, Guangli BAI. Influencing factors of thermal property parameter testing of lithium-ion batteries based on accelerating rate calorimeters [J]. Energy Storage Science and Technology, 2025, 14(4): 1596-1602.
[12]	Zuolin DONG, Jinyan SONG, Zidi MENG. Lithium-ion battery life prediction based on mode decomposition and deep learning [J]. Energy Storage Science and Technology, 2025, 14(4): 1645-1653.
[13]	Zhiming CHEN, Aimin CHU, Ziyu ZHOU, Yuping Zhao, Youming CHEN. Preparation and performance of Li-rich cathode material by carbon-containing droplet combustion [J]. Energy Storage Science and Technology, 2025, 14(4): 1362-1368.
[14]	Jinming YUE, Yuanli LIU, Yixia CHEN, Xiqian YU, Hong LI. Study on the separation conditions of lithium ion battery electrolyte by GC-MS detection [J]. Energy Storage Science and Technology, 2025, 14(4): 1564-1573.
[15]	Peng WANG, Jun ZHOU, Xing WU, Tao LIU. Remaining useful life prediction of a lithium-ion battery based on a cheetah optimization-extreme learning machine with improved Sine chaotic mapping [J]. Energy Storage Science and Technology, 2025, 14(4): 1603-1616.